Khinchine’s theorem and Edgeworth approximations for weighted sums

Research output: Contribution to journalArticlepeer-review

Abstract

Let F n denote the distribution function of the normalized sum of n i.i.d. random variables. In this paper, polynomial rates of approximation of F n by the corrected normal laws are considered in the model where the underlying distribution has a convolution structure. As a basic tool, the convergence part of Khinchine’s theorem in metric theory of Diophantine approximations is extended to the class of product characteristic functions.

Original languageEnglish (US)
Pages (from-to)1616-1633
Number of pages18
JournalAnnals of Statistics
Volume47
Issue number3
DOIs
StatePublished - Jan 2019

Bibliographical note

Funding Information:
Received October 2017; revised May 2018. 1Supported in part by the NSF Grant DMS-1612961 and the Russian Academic Excellence Project “5-100.” MSC2010 subject classifications. 60F05. Key words and phrases. Central limit theorem, Edgeworth approximations.

Funding Information:
1Supported in part by the NSF Grant DMS-1612961 and the Russian Academic Excellence Project “5-100.” We would like to thank the referee for a careful reading of the manuscript and useful remarks.

Publisher Copyright:
© Institute of Mathematical Statistics, 2019.

Keywords

  • Central limit theorem
  • Edgeworth approximations

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